A note on local center manifolds for differential equations with state-dependent delay

Abstract

In this note we consider local invariant manifolds of functional differential equations $x^{\prime}(t)=f(x_{t})$ representing differential equations with state-dependent delay. Starting with a local center-stable and a local center-unstable manifold of the functional differential equation at a stationary point, we construct, by a straightforward application of the Implicit Mapping Theorem, a local center manifold.